Question: Solve for $p$. Reduce any fractions to lowest terms. Don't round your answer, and don't use mixed fractions. $-7p-4 > 26p -94$
Solution: $\begin{aligned}-7p-4 & > 26p -94 \\\\ -7p&> 26p-90 &(\text{Add } 4 \text{ to both sides}) \\\\ -33p &> -90 &(\text{Subtract } 26p \text{ from both sides})\\\\ 33p&< 90&(\text{Multiply both sides by }-1)\\\\ p&<\dfrac{30}{11}&(\text{Divide both sides by }33 \text{ and simplify}) \end{aligned}$ [Why did the inequality sign flip when we multiplied by -1?] In conclusion, the answer is $p < \dfrac{30}{11}$.